As mentioned before, in order to describe the (extended) monstrous moonshine picture \(\mathfrak {M}\)  (resp. \(\mathfrak {M}^e\) ) we work through the list of 171 moonshine groups \(n|h+e,f,\hdots \)  as given in [1]} (that is, Figure REF  above) and determine for each of them all classes appearing in the \((n|h)\) -serpent (resp. in the \((N|1)\) -snake where \(N=h.n\) ). The number classes of \(\mathfrak {M}\)  and \(\mathfrak {M}^e\)  are the same and are all divisors of the occurring \(N\) . For each of these number classes we next determine the set of divisors of 24 for which primitive roots of unity appear with center the given number class. These sets will then determine the local structure in that number class of \(\mathfrak {M}\)  (resp. \(\mathfrak {M}^e\) ).
